Logic is reason; the original Greek term means 'pertaining to logos', where 'logos' apparently means something like 'reason', 'proportion', 'order'; it is also the Greek word for 'word' - for instance, in the Biblical phrase 'In the beginning was the word'.

Logic is concerned with the truth of statements about the world.
It is based on the insight that we can derive nontrivial information on the world by means of thought: that we can become aware of truths about the world purely by combining information in our minds. Such combination is called reason and an instance of it is called a logical argument.

We all use logic in daily life, we all think and argue. In ancient Greek and Roman times, reason was considered an advanced skill, essential to a good man's education; the extreme emphasis placed on deductiveargument by thinkers such as Socrates and the sophists, and the ground-breaking mathematical work by Euclid and others, have been major forces in shaping our Western civilization.

To the Greeks and Romans, there wasn't a clear-cut distinction between rhetorics (the art of speech/debate) and science (the discovery of truths about the world). Perhaps this is really the distinction between deduction and induction.

The proper analysis of logical arguments is essential to rhetorics, and our knowledge on this matter really hasn't advanced all that much in the last 2000 years; e.g. we still use Roman terminology to describe common logical fallacies. But in science, formal reasoning has seen immense progress: mathematical reasoning has advanced far beyond the simple geometry and calculus known to the Greeks. Mathematics is also applied to logic itself: probability theory is a way to model reasoning with quantifiable uncertainty, formal mathematical logic approaches qualitative reasoning as a computational process.

People who don't know what the word Logic means but insist on using it as if it were magical really get on my nerves. Logic is not the same as Common Sense, and while what one person’s common sense tells him another person may reject, if they stick to formal logic they can always reach a joint conclusion.

There’s a battle going on in E2, just like in real life, between people who seem more-or-less capable of thinking rationally (and of taking a scientific point of view), and those who are not. The people who can think rationally aren’t nicer than those who can’t, and are not necessarily better artists or friends. They do, however, explain the world in a way that they can all agree upon, and that leads humanity to many accomplishments (not on a moral, but on a technological level). For a thread of rants on this stuff, including my own, you can go here.

8. Natural selection has severe logical inconsistencies.
Natural selection has these and many other logical inconsistencies: (a.) Although evolutionists say that organisms are suited for their environment because they evolved into it, being suited for the environment is much better explained by the fact that they were created for the environment rather than that they evolved into it. (b.) The fact that living things have similar patterns and design points to a common designer better than to a common ancestor. In fact, such variety in the world could not have been produced if we all come from the same ancestor. (c.) If we all come from the same ancestor, we would all be murderers and cannibals by the simple act of killing a cow. (d.) While small and underdeveloped things do become grown and developed (a baby to an adult, a seed to a tree) it is also true that the small and underdeveloped first come from the developed (a baby from its parents, a seed from a tree). The pattern of growth is circular not simply from the crude to the developed as natural selection proposes. (e.) Our needs exceed those of survival. Needs for love and friendship, for example, cannot be explained if all that we do is for survival. (f.) Order and interdependence in the world argues for a designed and against chance.

Does everyone here notice what I notice? Not one logical inconsistency. Not once does the writer refer us to an evolutionary claim and have us follow the idea ‘till we reach a contradiction. I’m not talking about the fact that formal logic wasn’t used – even free form logic has nothing to do with the above text. So lets all try to understand the following idea (I’m writing this in bold so we all get it):

“Logic” does not mean making assertions that seem to make sense to us in a particularly smug way.

Logic has rules, and we may be using logic when we are using these rules.

Now, some of the claims in the above quote may appeal to a certain kind of common sense, and it’s OK to use them in an argument (wrong as they are, imho). But if I may add an additional contribution, small as it may be, to the way people argue/discuss things on E2 :

So, to sum this whole thing up, If you people want to give emotional reasons for things, if you want to state your opinion in general or give an example – you’re welcome to. However, don’t go around calling that logic.

Logic is about creating rules and assumptions ('axioms') and following the rules to create new rules.

It's sort of like a game, you create the rules, and you follow them to see what happens ('derive').

Mathematics is a obviously a branch of logic. You start with defining numbers like 0,1,2,3 (Peano axioms) etc. and then work out where it leads you. But that's obvious.

Far less obviously, religion; contrary to most people's opinion, is also logical. You start with a concept of God and a few other assumptions and work out what happens as a result, what it tells you about life. But the question is whether it is true.

A good question is whether people are logical or not. I believe that, except for insane people, the bottom line is that human beings are inherently pretty logical- they follow rules, they essentially think. So, logic is what people do.

But that isn't really the issue. The real question is the one of truth.

So let's talk about truth. In logic truth has a technical meaning.

It means that something is derivable given the assumptions and the rules. You can prove it, given the axioms.

But most people use the word 'truth' quite differently. Most people use the word truth to mean 'axiom' or 'something I assume to correspond to reality'. That's quite different, but related.

So the real and far more interesting question is what is true, in the everyday sense of the word, so: is there a 'God', is there life after death, what does 'moral' mean; do they fancy me, do they care about me, is it good to eat, how do I get as much money as Bill Gates, what is life all about, would she slap me if I ask that, what is the truth?

The laws of logic have been used in a variety of ways by philosophers in the past. Under the guise of human Reason, logic itself has been used as the epistemology of among others popular philosophers Aristotle and Rene Descartes. Interestingly enough, the rules of logic themselves have recently come under attack by the philosophy of postmodernism, mainly because of Aristotle and Descartes' assumption of their truth or correctness. Exactly where we get the basis of logic is really the sticking point for postmodernists, and therefore they correctly choose to not subject themselves to its bounds. Exactly how consistently they can do this varies. For anyone interested in the basis of logic, you cannot go wrong reading the works of Francis Schaeffer - he does a fantastic job of explaining the basis for logic and a proper view of Epistemology, Metaphysics, and Ethics.

What is Logic?

It is perhaps a slight miscomprehension to link logic totally with what is true and what is false. Although notions of truth are involved, logic is more concerned ultimately with the validity of arguments, and the consistency of statements. Logic is a tool we can use to test whether a particular argument is valid or not.

Arguments:

Arguments normally consist of a set of statements, known as premises, and a conclusion. The nature of an argument is such that if the premises are true, then the conclusion that follows from them must also be true. An often quoted example is:

It is clear to see that if statement 1) is true and statement 2) is true, then there is no way that 3) can be false. We therefore have a valid argument. Now, we must not get the idea of a valid argument confused with the idea of a good argument. Let's take the following example:

1) All men can fly like Superman and have six legs.2) Socrates is a man.3) Therefore Socrates can fly like Superman and has six legs.

Logical Possibility:

If something is logical, then it does not necessarily mean that it is true in the world, or even probable. To help gain a concept of logical possibility, it is helpful to consider the idea of "possible worlds".

Let us imagine that there are very many, perhaps an infinite number of, "worlds". With this system, we can imagine that things are different in each. One of these worlds is the "actual world" - i.e., the one in which we live - but all the others are our own creation. Now, for something to be logically possible, all we need is for it to be able to happen in one of these worlds we created. Now, take the argument I quoted earlier:

1) All men can fly like Superman and have six legs.2) Socrates is a man.3) Therefore Socrates can fly like Superman and has six legs.

Now in our possible worlds, we can create one where men do in fact fly like Superman and have six legs. It is not the actual world of course, but that does not matter here. The possible worlds are a way of rejecting any set of statements of an argument that contain a contradiction. If an argument has a contradiction within it, then it cannot be possible in any possible world. Here is an example to demonstrate:

1) All lemons are yellow all over.2) This is a lemon.3) Therefore this is blue all over.

Clearly, there is a contradiction here. There is no possible world that we can create where we have a lemon that is both yellow all over and blue all over. This is therefore a logical impossibility. We can use ideas of logical possibility to define validity:

A set of statements forms a valid argument if there is no possible world in which the premises are true, and the conclusion false.

It follows from this that any conclusion can follow a contradiction and it still be a valid argument. This is because there is no possible world where the premises are true and the conclusion false since the premises can never be true anyway.

Necessary Truth:

A necessary truth, also known as a tautology, is something that is true in all possible worlds. For instance, mathematical laws are necessarily true. We cannot conjure up an imaginary world where two plus two does not equal four. The number it equals in a world might not be called "four", but it will be the same thing, just as water is the same as H2O. An example of a necessary statement outside the realms of mathematics would be something along the lines of:

"My shoes are black all over, or they are not black all over."

It is clear that there is no possible situation where this is not true.

If a necessary truth should be the conclusion of an argument, then that argument is always valid because the conclusion can never be false in any possible world. For instance:

1) My shoes are black all over.2) My shoes are brown all over.3) Therefore two plus two equals four.

Here there is an obvious contradiction in the premises, yet the conclusion is a necessary truth, so the argument is valid. A rule of logic is that anything entails a tautology.

Conversely, it is another rule that anything can follow a contradiction, as this is another situation where it can never be the case that the premises are true and the conclusion false.

Wilfred Hodges, "Logic"

Thanks to tdent for pointing out that I neglected to mention that anything can follow a contradiction.

The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning.

Logic is science of the laws of thought, as that is, of the necessary conditions to which thought, considered in itself, is subject.
Sir W. Hamilton.

Logic is distinguished as pure and applied. " Pure logic is a science of the form, or of the formal laws, of thinking, and not of the matter. Applied logic teaches the application of the forms of thinking to those objects about which men do think. "